A characterization of semiampleness and contractions of relative curves

2000/01/31 by Stefan Schroeer
Mathematics · #math.AG #msc:14A15 #msc:14C20 #msc:14H10

paper · pdf

published as Kodai Math. J. 24 (2001), 207--213 · 6 pages. Minor changes. To appear in Kodai Math. J

arxiv created 2001/04/21 · arxiv updated 2009/11/30

Abstract

A line bundle with a base-point-free multiple is called semiample. I give a cohomological characterization of semiample line bundles. The result is a common generalization of the Fujita-Zariski criterion for semiampleness and the Grothendieck-Serre characterization of ampleness. Applying the Fujita-Zariski Theorem, I characterize contractible curves in 1-dimensional families.

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